Question

第二问怎么求m？

Answer 1

(2)x=m+√3y,
代入x^2+y^2=2x,得
m^2+2√3my+4y^2=2m+2√3y,
整理得4y^2+2√3(m-1)y+m^2=0,
△/4=3（m-1)^2-4m^2=-m^2-6m+3,
y=[-√3(m-1)土√(-m^2-6m+3)]/4,
设A(x1,y1),B(x2,y2),
|PA|:|PB|=|y1|:|y2|=2,
所以y1=土2y2,y1y2=m^2/4>=0,
所以y1=2y2,即[-√3(m-1)+√(-m^2-6m+3)]/4=[-√3(m-1)-√(-m^2-6m+3)]/2，
所以3√(-m^2-6m+3)=-√3(m-1),
m<=1时平方得3(-m^2-6m+3)=m^2-2m+1,
整理得4m^2+16m-8=0,
化简得m^2+4m-2=0,
解得m=-2土√6.